Transmission of precoding codebook over an air interface

ABSTRACT

Embodiments of the present invention include a system for transmitting a precoding codebook over an air interface. The system includes a first station configured to signal a set of indicators via at least one antenna to a second station from which the precoding codebook is derived at the second station based on the signaled set of indicators. The set of indicators includes less information than the precoding codebook.

BACKGROUND

Base stations in wireless communication systems provide wirelessconnectivity to users within the geographic area, or cell, associatedwith the base station. The wireless communication links between the basestation and each of the users typically include one or more downlink (orforward) channels for transmitting information from the base station tothe mobile unit and one or more uplink (or reverse) channels fortransmitting information from the mobile unit to the base station.Multiple-input-multiple-output (MIMO) techniques may be employed whenthe base station and, optionally, the user terminals include multipleantennas. For example, a base station that includes multiple antennascan transmit multiple independent and distinct signals to multiple usersconcurrently and on the same frequency band. MIMO techniques are capableof increasing the spectral efficiency of the wireless communicationsystem approximately in proportion to the number of antennas availableat the base station.

It is well known that using a plurality of antennas instead of oneantenna adds an additional spatial multiplex dimension to thecommunication system. One way to exploit the spatial dimension ofmultiple antennas in a MIMO system is to multiply complex weights tosignals before transmitting the signals over each of the individualantennas of the multiple antennas at the base station. The complexweights are arranged in vectors, in which the vectors of complex weightsform matrices. A set of matrices defined in a specific applicationscenario is called a codebook. An application scenario is related to avariety of parameters influencing the optimal codebook. Such parametersinclude antenna configuration parameters such as spacing andpolarization and parameters characterizing the radio channel such asvehicular speed and scattering environment, for example. The operationperformed on the signal before being transmitted from the base stationis called precoding. Codebooks form an integral part of current mobileradio standards such as the first version (“Release 8”) of long termevolution (LTE) of the universal mobile telecommunication system (UMTS),as well as Worldwide Interoperability for Microwave Access (WiMAX) andUltra Mobile Broadband (UMB), for example. The selection of anappropriate codebook is a function of the effective scenario and mayvary over time. The effective scenario is a function of a large varietyof parameters such as antenna configuration and radio environment and ina mobile radio environment that changes over time. As a consequence, theoptimal codebook is also a function of time.

In order to deal with a large variety of scenarios (e.g., antennaconfigurations, and radio propagation channel conditions) encountered inreal-world scenarios, a codebook may have to be changed or modified.Therefore, the possibility for mobile terminals to download a codebookused for precoding by base stations has been proposed for variousapplications in order to cope with all kinds of channel and antennascenarios. The Ultra-Mobile Broadband standard developed in 3GPP2includes downloadable codebooks. However, the signaling procedures bywhich such downloads are accomplished are cumbersome. For example,conventional methods of downloading codebooks must transmit a complexnumber for every element of every matrix in the codebook.

SUMMARY

The present invention relates to a system for transmitting a precodingcodebook over an air interface. The system includes a first stationconfigured to signal a set of indicators via at least one antenna to asecond station from which the precoding codebook is derived at thesecond station based on the signaled set of indicators. The set ofindicators includes less information than the precoding codebook. Thefirst station may be a base station, and the second station may be auser device, or vice versa.

In one embodiment, the set of indicators includes a first set ofcodewords such that a second set of codewords can be derived at thesecond station based on a mirror operation.

In another embodiment, the set of indicators includes a sub-set ofcomplex elements of the precoding codebook, where each complex elementof the sub-set has a predefined magnitude or phase.

In another embodiment, the set of indicators includes a sub-set ofcomplex elements of the precoding codebook, where the complex elementsof the sub-set are dependent upon each other. The at least one antennamay include a plurality of antennas. For example, a first antenna of theplurality of antennas is assigned a first antenna weight and asubsequent antenna is assigned a second weight. The second weight is afunction of the first antenna weight and an antenna weight of apreceding antenna. The function may be a product, or a relationship suchthat the ratio of the second weight and the first weight is equal to theratio of the first weight and the preceding antenna weight.

In another embodiment, the set of indicators includes a base phase forone of the plurality of antennas and an offset phase for other antennasof the plurality of antennas.

In another embodiment, the precoding codebook is a hierarchical codebookand the set of indicators includes an indicator indicating a level of ahierarchy and a set of matrices among matrices comprising the indicatedlevel. The plurality of antennas may be a linear array or a circulararray, for example. Also, the set of indicators may include an indicatorto a first codebook and at least one indicator to at least one othercodebook such that the hierarchical codebook can be derived based on acomposition operation between the indicator to the first codebook andthe at least one indicator to the at least one other codebook.

Embodiments of the present invention also include a system for receivinga precoding codebook over an air interface from a first station. Thesystem may include a second station configured to derive the precodingcodebook based on a set of indicators received at the second stationfrom the first station. The set of indicators includes less informationthan the precoding codebook.

In one embodiment, the second station derives a second set of codewordsfrom the set of indicators being a first set of codewords based on amirror operation.

In another embodiment, the second station derives the precoding codebookfrom the set of indicators being a sub-set of complex elements of theprecoding codebook, where each complex element of the sub-set has apredefined magnitude or phase resolution.

In another embodiment, the second station derives the precoding codebookfrom the set of indicators being a sub-set of complex elements of theprecoding codebook, where the complex elements of the sub-set aredependent upon each other.

In another embodiment, the precoding codebook is a hierarchical codebookand the second station derives the hierarchical codebook from the set ofindicators being an indicator indicating a level of a hierarchy and aset of matrices among matrices comprising the indicated level. Also, theset of indicators may include an indicator to a first codebook and atleast one indicator to at least one other codebook, and the secondstation derives the hierarchical codebook based on a compositionoperation between the indicator to the first codebook and the at leastone indicator to the at least one other codebook.

Embodiments of the present invention also include a method fortransmitting a precoding codebook over an air interface from a firststation. The method includes signaling a set of indicators from thefirst station via at least one antenna to a second station from whichthe precoding codebook is derived at the second station based on thesignaled set of indicators. The set of indicators includes lessinformation than the precoding codebook.

Example embodiments of the present invention also include a method forreceiving a precoding codebook over an air interface from a firststation. The method includes deriving at a second station the precodingcodebook based on a set of indicators received at the second stationfrom the first station. The set of indicators includes less informationthan the precoding codebook.

In one embodiment, the deriving step includes deriving a second set ofcodewords from the set of indicators being a first set of codewordsbased on a mirror operation.

In another embodiment, the deriving step includes deriving the precodingcodebook from the set of indicators being a sub-set of complex elementsof the precoding codebook, where each complex element of the sub-set hasa predefined magnitude or phase resolution.

In another embodiment, the deriving step includes deriving the precodingcodebook from the set of indicators being a sub-set of complex elementsof the precoding codebook, where the complex elements of the sub-set aredependent upon each other.

In another embodiment, the precoding codebook is a hierarchical codebookand the deriving step includes deriving the hierarchical codebook fromthe set of indicators being an indicator indicating a level of ahierarchy and a set of matrices among matrices comprising the indicatedlevel. Also, the set of indicators may include an indicator to a firstcodebook and at least one indicator to at least one other codebook,where the deriving step derives the hierarchical codebook based on acomposition operation between the indicator to the first codebook andthe at least one indicator to the at least one other codebook.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will become more fully understood from the detaileddescription given herein below and the accompanying drawings, whereinlike elements are represented by like reference numerals, which aregiven by way of illustration only and thus are not limiting of thepresent invention, and wherein:

FIG. 1 illustrates a wireless communication system according to anexample embodiment of the present invention;

FIG. 2 illustrates an example of a codebook to be compressed based on amirror operation according to an embodiment of the present invention;

FIG. 3 illustrates a linear array of antennas according to an embodimentof the present invention;

FIG. 4 illustrates an example of a QPSK system featuring symbols withequal magnitude according to an embodiment of the present invention;

FIG. 5 illustrates a 64QAM system according to an embodiment of thepresent invention;

FIG. 6 illustrates a linear array of antennas with complex weightingaccording to an embodiment of the present invention;

FIG. 7 illustrates an embodiment of the hierarchical codebook accordingto the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

Various embodiments of the present invention will now be described morefully with reference to the accompanying drawings in which someembodiments of the invention are shown. Like numbers refer to likeelements throughout the description of the figures.

As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”,“comprising,”, “includes” and/or “including”, when used herein, specifythe presence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

It should also be noted that in some alternative implementations, thefunctions/acts noted may occur out of the order noted in the figures.For example, two figures shown in succession may in fact be executedsubstantially concurrently or may sometimes be executed in the reverseorder, depending upon the functionality/acts involved.

Embodiments of the prevent invention relate to reliable and efficienttransmission of codebooks by utilizing signaling techniques, whereredundancies that exist in codebook entries are reduced. As a result, anamount of data representing the codebook that is transmitted to a userdevice from a base station is reduced.

FIG. 1 illustrates a wireless communication system 100 according to anembodiment of the present invention.

The wireless communication system 100 includes a base station 105 thatprovides wireless connectivity to one or more users 110 (only one shownin FIG. 1) over corresponding air interfaces 115 (e.g., 115(1)-115(n)).However, persons of ordinary skill in the art should appreciate that thepresent disclosure is not limited to wireless communication systems 100that use base stations 105 to provide wireless connectivity. Inalternative embodiments, the wireless communication system 100 may useother devices to provide wireless connectivity, such as base transceiverstations, base station routers, WiMAX or WiFi access points, accessnetworks, and the like. The user 110 may include but is not limited to auser equipment (EU), a mobile station, a fixed or mobile subscriberunit, a pager, a cellular telephone, a personal digital assistant (PDA),a computer, or any other type of user device capable of operating in awireless environment.

Techniques for establishing, maintaining, and operating air interfaces115 to provide uplink and/or downlink wireless communication linksbetween the base station 105 and the users 110 are known in the art andin the interest of clarity only those aspects of establishing,maintaining, and operating the air interfaces 115 that are relevant tothe present disclosure will be discussed herein.

The base station 105 includes multiple antennas 120 for transmittingand/or receiving information over the air interfaces 115. Although threeantennas 120 (e.g., 120(1), 120(2), 120(n _(T))) are depicted in FIG. 1,persons of ordinary skill in the art should appreciate that the basestation 105 is not limited to any particular number of antennas 120.Moreover, persons of ordinary skill in the art should appreciate that,in some embodiments, the users 110 may also include multiple antennas.The base station 105 may therefore employ multiple-input-multiple-output(MIMO) techniques so that the multiple antennas 120 can transmitmultiple independent and distinct signals to the users 110 concurrentlyand on the same frequency band using spatially multiplexed channels ofthe air interfaces 115.

The base station 105 includes a precoder 125 that maps signals to betransmitted to each user 110 onto the available channels usingpre-coding matrices associated with the user 110. The precoding matrixis generated based on feedback, for example, the vector quantizationfeedback obtained from each user 110. Other forms of feedback other thanvector quantization are well within example embodiments of the presentinvention. For example, the feedback may include an index of an entry ina codeword table. The base station 105 may therefore store codebooks 130of matrices, Ci, associated with each user 110 that is connected to thebase station 105. The codebooks 130 include complex weights that arearranged in vectors, in which the vectors of complex weights formmatrices. A set of matrices defined in a specific application scenariois called a codebook. In the case of uplink precoding, the user 110 canalso include the precoder 125. In such a case, the user 110 may mapsignals to be transmitted to the base station 105 onto the availablechannels using pre-coding matrices.

Table 1, depicted below, illustrates an example of a codebook for twoantennas with four entries. As a result, the codebook illustrated belowincludes four precoding vectors (or “codewords”). The parameters θ₁ . .. θ₄ can be interpreted as directions in the case of λ/2 element spacingbetween the two antennas, for example.

TABLE 1 Example codebook for 2 transmit antennas Beam Index Weight 1: w₁Weight 2: w₂ 1 1 exp(−jπ sin(θ₁)) 2 1 exp(−jπ sin(θ₂)) 3 1 exp(−jπsin(θ₃)) 4 1 exp(−jπ sin(θ₄))

Each of the codewords may include at least two weights: w₁ and w₂. Inthis example, w₁ has a value of 1 for each of the beam indices. Thevalues for w₂ depend on the element spacing of the antennas. Each of thecodewords may also include a beam index number associated with weightsw₁ and w₂. The example codebook depicted in Table 1 is for illustrativepurposes only, where other types of codebooks are well within theembodiments of the present invention. For instance, codebooks of thepresent disclosure encompass any number of weights and/or valuesassociated with each weight.

Referring back to FIG. 1, the system may start with a predefined fixedcodebook known at both the user 110 and the base station 105 of thecommunication link in order to be able to use precoding techniquesbefore the codebook download. Thereafter, the base station 105 transmitsthe codebooks 130 over an air interface to each user 110 in order forthe user to first generate feedback information based on the transmittedcodebook and subsequently to receive signals precoded with an entry ofthe transmitted codebook 130. For example, the user 110 may transmitfeedback bits representative of the selected codebook and/or codeword tothe base station 105, which may transmit information to the user 110using pre-coding matrices determined based on the feedback from the user110 and any other users in the system 100. The base station 105 may usethe additional feedback provided by each user 110 to update thecodewords and/or codebook associated with each user 110.

However, before transmission of the set of codebooks 130, the basestation 105 compresses the codebook for efficient transmission to theuser 110. Similarly, the user 110 may compress the codebook fortransmission to the base station 105. The base station 105 signals a setof indicators from which the entire codebook may be uniquely derived.The set of indicators includes less information than the information ofthe entire codebook. As a result, the amount of the signaling issubstantially reduced compared to explicit signaling of the entirecodebook. Different types of compression for precoding codebooks aredescribed below according to embodiments of the present invention.

FIG. 2 illustrates an example of a codebook 130 to be compressed basedon a mirror operation according to an embodiment of the presentinvention. For example, FIG. 2 shows four codewords, where each codewordis associated with an entry index number. Each codeword includes aplurality of weights (or elements) comprising a weight vector. Forexample, the codeword associated with entry index 1 includes weightvector W10, W11, W12 and W13.

According to this embodiment, the base station 105 of FIG. 1 signals afirst set of codewords of the codebook 130 to the user 110 via theplurality of antennas 120. The first set of codewords represents only aportion of the codebook 130. A second set of codewords is obtained atthe user 110 by mirroring the first set of codewords. As a result, thebase station 105 only transmits part of the codebook 130, whereas theentire codebook 130 may be obtained at the user 110 based on a mirroringoperation, which is explained below.

For example, the codebook 130 may be separated into a first set ofcodewords and a second set of codewords. If the total number ofcodewords equals K, the codewords of the codebook 130 may be dividedinto two sets of K/2 codewords, where each half is associated with thefirst and second sets, respectively. The second set of codewords isassigned to be “mirrors” of the first set of codewords, or vice versa,based on symmetries associated with the plurality of antennas 120, whichare explained with reference to FIG. 3. In the example of FIG. 2, theweight vectors associated with entry indices 3 and 4 are assigned to be“mirrors” of the weight vectors associated with entry indices 1 and 2.In this example, the base station 105 signals the first set of codewordsassociated with entry indices 1 and 2, and the user 110 receives thecodewords associated with entry indices 1 and 2, and obtains the secondset of codewords associated with entry indices 3 and 4 based on themirroring operation, which is explained below.

After the user 110 receives the codewords associated with entry indices1 and 2, the user 110 mirrors these codewords by reversing the elementsin the first set of codewords. For example, the weight vector associatedwith entry index 1 includes weights W10, W11, W12, W13. The user 110would obtain the codeword associated with entry index 4 by flipping theelements of “W10, W11, W12, W13” to obtain W13, W12, W11, and W10, whichis the codeword associated with entry index 4. The same operation isperformed on the codeword associated with entry index 2 to obtain thecodeword associated with entry index 3. As a result, the base station105 transmits a set of indicators, which represents approximately halfof the entire codebook 130, and the user 110 is able to obtain the otherhalf based on the mirroring operating described above. Also, this mirroroperation can also exploit symmetries in the overall codebook matrix,which may be of hermitian nature, thus being equal to its conjugatetranspose. For example.

FIG. 3 illustrates a linear array of antennas according to an embodimentof the present invention. The linear array of antennas includes aplurality of antennas 120-antenna 120(1), antenna 120(2), antenna120(3), and antenna 120(4), where each antenna is separated by adistance d. The plurality of antennas 120 may be used in a MIMO systemas explained above. Each of the plurality of antennas 120 includesantennas weights used during precoding at the precoder 125. Thecodewords of the codebook 130 are based on the antenna weights of theplurality of antennas 120. Because antenna 120(1) and antenna 120(2) maybe symmetrical with antenna 120(4) and antenna 120(3), the antennaweights of antennas 120(3) and 120(4) may be mirrors of antennas 120(2)and 120(1). These symmetries are exploited in order to efficientlytransmit a codebook 130 to the user 110. Embodiments of the presentinvention are not only limited to a linear array of antennas, but mayalso encompass other types of antenna arrangements that exhibitsymmetrical features such as a circular array of antennas orcross-polarized antennas, for example.

According to another embodiment of the present invention, the basestation 105 signals a sub-set of complex elements of the codebook 130,where each of the complex elements within the sub-set has a certainpredefined magnitude and/or phase. For example, the base station 105signals a set of indicators from which the entire codebook may beuniquely derived. The set of indicators includes less information thanthe information of the entire codebook. As a result, the amount of thesignaling is substantially reduced compared to explicit signaling of theentire codebook. The complex elements may be quadrature amplitudemodulation (QAM) and/or phase-shift keying (PSK) symbols, for example.For instance, the individual elements of the vectors and matricesconstituting the codebooks 130 are complex numbers. Although complexnumbers from the whole complex plane may be used as elements incodebooks, the elements of the codewords are often taken from a limitedset of complex numbers called the alphabet, for example. This alphabetis based on a well-known modulation system. Because the used alphabet isfinite, the set of complex numbers used for downloading the codebook maybe indexed. As a result, whereas the alphabet is transmitted in highresolution or is predefined, the actual codebook and respective scalingfactors are transmitted as a set of indices thereby reducing the amountof information needed for transmission. The user 110 derives the entirecodebook 130 based on the sub-set of complex elements throughdemodulation.

FIG. 4 illustrates an example of a quadrature phase-shift keying (QPSK)system 140 featuring symbols with equal magnitude according to anembodiment of the present invention. In this example, the individualelements of the entire codebook are taken from the set of 4 complexnumbers as defined in FIG. 4. As a result, the amount of informationtypically needed for the transmission of each element of the codebook130 may be reduced to only two bits. Namely, each complex element isrepresented by a different two bit combination. The two bits representsan index in the sub-set of complex elements signaled from the basestation 105 to each user 110, where the sub-set of elements includesfour complex numbers, as shown in FIG. 4.

FIG. 5 illustrates a 64QAM system 150 according to an embodiment of thepresent invention. In this example, the individual elements of theentire codebook are taken from the set of 64 complex numbers as definedin FIG. 5. As a result, the amount of information typically needed forthe transmission of each element of the codebook 130 may be reduced toonly six bits. Each possible combination of the six bits represents thesub-set of complex elements signaled from the base station 105 to eachuser 110, where the sub-set of elements may include at least the 64complex numbers, as shown in FIG. 5. It will be appreciated that thecompression techniques of FIGS. 4 and 5 may be applied to other forms ofmodulation besides QPSK and 64QAM.

According to another embodiment of the present invention, the basestation 105 signals a sub-set of elements within codewords of acodebook, where elements of the transmitted sub-set are dependent oneach other. Based on this dependency, the user 110 may obtain the entirecodebook. For example, the base station 105 signals a set of indicatorsfrom which the entire codebook may be uniquely derived. The sub-set ofcomplex elements includes less information than the information of theentire codebook. This operation is further explained with reference toFIG. 6.

FIG. 6 illustrates a linear array of antennas with complex weightingaccording to an embodiment of the present invention. The linear array ofantennas includes a plurality of antennas 120, where each of theplurality of antennas 120 is separated by equal distance, as indicatedby distance d. According to this embodiment, the first antenna 120(1)may be assigned a specific antenna weight. The antenna weights of eachof the subsequent antennas are gained by (another) multiplication of thefirst antenna weight to the weight of the preceding antenna. AlthoughFIG. 6 illustrates specific antenna weights for each of the plurality ofantennas 120, any type of complex value of the first antenna weight andany other algorithm providing the remaining antenna weights are wellwithin the embodiments of the present invention.

Based on this arrangement shown in FIG. 6, the base station 105 only hasto transmit a subset of elements in a codebook. For example, referringto FIG. 6, the base station 105 may signal elements of associated withantenna 120(1). The user 110 obtains the entire codebook byappropriately modifying the transmitted elements associated with antenna120(1) to obtain the other elements associated with antennas 120(2) to120(4).

According to another embodiment of the present invention, the basestation 105 may signal a starting phase for one of the plurality ofantennas 120 and signal incremental relative phase shifts for allneighbor array elements. For example, the base station 105 signals a setof indicators being a base phase for one antenna and an offset phase forthe other antennas from which the entire codebook may be uniquelyderived. The set of indicators includes less information than theinformation of the entire codebook. As a result, the amount of thesignaling is substantially reduced compared to explicit signaling of theentire codebook. For example, a base antenna may be assigned with a basephase ph1, whereas the phase offset for the next antenna in onedimension or next antennas in additional dimensions may be provided withan offset phase delta_ph2. The distinct antenna is predetermined betweenthe base station 105 and each user 110. The user 110 may compute theprecoding weights for the entire codebook based on the beam directionand antenna spacing (relative to the carrier wavelength) using standardgeometrical procedures. For the special case of channels with relativelylow angle spread, phase shifts could be designed to relate directly tothe direction of the resulting beam following standard geometricalprocedures. Therefore, the set of indicators being signaled from thebase station 105 to each user 110 may include a base phase for one ofthe plurality of antennas and an additional offset for the otherplurality of antennas. The user 110 may obtain the entire codebook 130based on the base phase for one of the plurality of antennas and theadditional offset for the other plurality of antennas.

According to another embodiment of the present invention, the codebooks130 may be a hierarchical codebook, as explained in U.S. patentapplication Ser. No. 11/754,624, filed May 29, 2007, which isincorporated by reference in its entirety herein. In other words, thecodebooks 130 associated with each user 110 may be part of thehierarchical codebook 130, e.g., each codebook is a part of a level 1 ofthe hierarchical codebook 130 that has L levels, where 0<or=l<or=L. Thehierarchical codebook 130 is organized such that each of the matrices ina relatively low level is associated with one of the matrices in thenext higher level.

FIG. 7 illustrates an embodiment of the hierarchical codebook 130.Referring to FIG. 7, the hierarchical codebook 130 may include threelevels. Although the hierarchical codebook 130 of FIG. 7 illustratesthree levels, the hierarchical codebook 130 may include any number oflevels greater than one. Each level indicates a set of codebook entriesdetailing a next higher level. For example, the codebook entriesassociated with level 1 include four codewords. Each codeword associatedwith level 1 includes 2 bits. At level 2, each codeword associated withlevel 1 includes four codewords. Each codeword associated with level 2includes 4 bits. Similarly, at level 3, each codeword associated withlevel 2 includes four more codewords. Each codeword associated withlevel 3 includes 8 bits. Therefore, within each level, the resolution ofthe codebook is increased by a factor of four.

B′<B bits are used to index 2^(B′) codewords within a given level, andthe remaining B−B′ bits are used to traverse between groups. B indicatesthe total number of feedback bits per interval. B′ indicates the numberof bits for a particular level. Referring to FIG. 7, the hierarchicalcodebook with 3 levels is indexed using a total of B=3 bits. B′=2 bitsselects the codebook within a group of 4 codewords, and the remaining 1bit indicates an “up” or “down” transition between levels.

Referring to FIG. 7, the second codebook (e.g., codebook of level 2)depends on the selection of a first code vector from a first codebook(e.g., codebook of level 1). A functional description of the codewordgeneration may be as follows:w=w_(a)∘w_(b) and w_(a)εCB_(a) w_(b)εCB_(b).

For example, a composition operation is performed between vectors w_(b)and w_(a) in the user 110 after retrieval of the codewords w_(b) andw_(a) from the storage space. Vectors w_(b) and w_(a) are vectors withina codebook 130. Each of the Vectors w_(b) and w_(a) includes codewordsrepresented by CB_(a) and CB_(b), respectively. The compositionoperation may include an element-wise multiplication. In theelement-wise multiplication, the matrices must have the same number ofrows and columns and the corresponding elements are element-wisemultiplied with each other.

According to an embodiment of the present invention, hierarchicalcodebooks 130 may be effectively compressed by defining each codeword asthe element-wise product of codewords drawn from different “parent”codebooks. In this embodiment, the base station 105 signals an indicatorof a level of the hierarchy and a set of indicators indicating a set ofmatrices from among the matrices comprising the indicated level. The setof indicators may be a bitmap. Based on the indicator and the set ofindicators indicating the set of matrices, the user 110 obtains the setof hierarchical codebooks based on an element-wise product of the set ofindicators indicating the set of matrices that comprise the indicatedlevel. The indication of the level together with the bitmap specifies asubset of codebook entries specifying a codebook.

“Children” codewords for any codeword w₁εC₁ of a parent level may beobtained based on Equation 1, listed below.

Equation 1: w₂=w₁∘w_(g), where w_(g)εG is an element of the parentcodebook G.

C₁ may denote the 4 codewords of a parent level (e.g., level 1), and the4 “children” codewords (e.g., level 2) may be obtained as theelement-wise product w₂=w₁∘w_(g), where w_(g)εG is an element of theparent codebook G.

As the number of levels of the hierarchy is increased, an arbitrarilylarge number of matrices are formed. By then selecting an arbitrarysubset of the matrices at a particular level, any arbitrary codebook canbe designed.

For example, the base codebook may include matrices with close spacingin the direction of a highest probability of a location of the user 110,and at least one matrix with a relatively more distant spacing in theouter regions on either side of the believed location of the user 110.This increases the robustness of the codebook against mobility of theuser 110. The signaling required in such an approach would consist onlyof a single integer indicating the level of the hierarchical codebookfrom which the set of matrices should be selected, and a bitmap oflength equal to the number of matrices at that level.

Although the embodiments described above illustrate a base stationsignaling a set of indicators to a user, embodiments of the presentinvention also include the situation where the user signals the set ofindictors to the base station. For example, a first station may signal aset of indicators to a second station, and the second station maysignals a set of indicators to the first station. Subsequently, thecodebook may be derived at the first station or the second station.

Variations of the embodiments of the present invention are not to beregarded as a departure from the spirit and scope of the embodiments ofthe invention, and all such variations as would be apparent to oneskilled in the art are intended to be included within the scope of thisinvention.

1. A system for transmitting a precoding codebook over an air interface,the system comprising: a first station configured to signal a set ofindicators via more than one antenna to a second station from which theentire precoding codebook is derived at the second station based only onthe signaled set of indicators, the set of indicators including lessinformation than the precoding codebook, wherein the set of indicatorsincludes a first set of codewords such that a second set of codewords isderived at the second station by a mirror operation based on symmetriesassociated with the more than one antenna.
 2. The system of claim 1,wherein the set of indicators includes a sub-set of complex elements ofthe precodirig codebook, wherein each complex element of the sub-set hasa predefined magnitude or phase.
 3. The system of claim 1, wherein theset of indicators includes a sub-set of complex elements of theprecoding codebook, wherein the complex elements of the sub-set aredependent upon each other.
 4. The system of claim 3, wherein the morethan one antenna includes a first antenna assigned a first antennaweight and a subsequent antenna is assigned a second weight, the secondweight being a function of the first antenna weight and an antennaweight of a preceding antenna.
 5. The system of claim 1, the set ofindicators including a base phase for one of the plurality of antennasand an offset phase for other antennas of the plurality of antennas. 6.The system of claim 1, wherein the precoding codebook is a hierarchicalcodebook and the set of indicators includes an indicator indicating alevel of a hierarchy and a set of matrices among matrices comprising theindicated level.
 7. The system of claim 1, wherein the precodingcodebook is a hierarchical codebook and the set of indicators includesan indicator to a first codebook and at least one indicator to at leastone other codebook such that the hierarchical codebook can be derivedbased on a composition operation between the indicator to the firstcodebook and the at least one indicator to the at least one othercodebook.
 8. The system of claim 1, wherein the first station is a basestation and the second station is a user device.
 9. A system forreceiving a precoding codebook over an air interface from a firststation, the system comprising: a second station configured to derivethe entire precoding codebook based only on a set of indicators receivedat the second station from more than one antenna at the first station,the set of indicators including less information than the precodingcodebook, the set of indicators includes a first set of codewords suchthat a second set of codewords is derived at the second station by amirror operation based on symmetries associated with the more than oneantenna.
 10. The system of claim 9, wherein the second station derivesthe precoding codebook from the set of indicators being a sub-set ofcomplex elements of the precoding codebook, wherein each complex elementof the sub-set has a predefined magnitude or phase.
 11. The system ofclaim 9, wherein the second station derives the precoding codebook fromthe set of indicators being a sub-set of complex elements of theprecoding codebook, wherein the complex elements of the sub-set aredependent upon each other.
 12. The system of claim 9, wherein theprecoding codebook is a hierarchical codebook and the second stationderives the hierarchical codebook from the set of indicators being anindicator indicating a level of a hierarchy and a set of matrices amongmatrices comprising the indicated level.
 13. The system of claim 9,wherein the precoding codebook is a hierarchical codebook and the set ofindicators includes an indicator to a first codebook and at least oneindicator to at least one other codebook, wherein the second stationderives the hierarchical codebook based on a composition operationbetween the indicator to the first codebook and the at least oneindicator to the at least one other codebook.
 14. A method fortransmitting a precoding codebook over an air interface from a firststation, the system comprising: signaling a set of indicators from thefirst station via more than one antenna to a second station from whichthe entire precoding codebook is derived at the second station basedonly on the signaled set of indicators, the set of indicators includingless information than the precoding codebook, wherein the set ofindicators includes a first set of codewords such that a second set ofcodewords is derived at the second station by a mirror operation basedon symmetries associated with the more than one antenna.
 15. The methodof claim 14, wherein the set of indicators includes a sub-set of complexelements of the precoding codebook, wherein each complex element of thesub-set has a predefined magnitude or phase.
 16. The method of claim 14,wherein the set of indicators includes a sub-set of complex elements ofthe precoding codebook, wherein the complex elements of the sub-set aredependent upon each other.
 17. The method of claim 14, wherein theprecoding codebook is a hierarchical codebook and the set of indicatorsincludes an indicator indicating a level of a hierarchy and a set ofmatrices among matrices comprising the indicated level.
 18. The methodof claim 14, wherein the precoding codebook is a hierarchical codebookand the set of indicators includes an indicator to a first codebook andat least one indicator to at least one other codebook such that thehierarchical codebook can be derived based on a composition operationbetween the indicator to the first codebook and the at least oneindicator to the at least one other codebook.
 19. A method for receivinga precoding codebook over an air interface from a first station, themethod comprising: deriving at a second station the entire precodingcodebook based only on a set of indicators received at the secondstation from more than one antenna at the first station, the set ofindicators including less information than the precoding codebook, theset of indicators includes a first set of codewords such that a secondset of codewords is derived at the second station by a mirror operationbased on symmetries associated with the more than one antenna.
 20. Themethod of claim 19, wherein the deriving step includes deriving theprecoding codebook from the set of indicators being a sub-set of complexelements of the precoding codebook, wherein each complex element of thesub-set has a predefined magnitude or phase.
 21. The method of claim 19,wherein the deriving step includes deriving the precoding codebook fromthe set of indicators being a sub-set of complex elements of theprecoding codebook, wherein the complex elements of the sub-set aredependent upon each other.
 22. The method of claim 19, wherein theprecoding codebook is a hierarchical codebook and the deriving stepincludes deriving the hierarchical codebook from the set of indicatorsbeing an indicator indicating a level of a hierarchy and a set ofmatrices among matrices comprising the indicated level.
 23. The methodof claim 19, wherein the precoding codebook is a hierarchical codebookand the set of indicators includes an indicator to a first codebook andat least one indicator to at least one other codebook, wherein thederiving step derives the hierarchical codebook based on a compositionoperation between the indicator to the first codebook and the at leastone indicator to the at least one other codebook.